On the limitations of low‐rank approximations in contact mechanics problems

Kiran Sagar Kollepara (1, 2, 3) , José M Navarro‐jiménez (4) , Yves Le Guennec (3) , Luisa Silva (2, 1) , José V Aguado (1, 2)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 Nantes Univ - ECN - École Centrale de Nantes
3 IRT Jules Verne - Institut de Recherche Technologique Jules Verne [Bouguenais]
4 UPV - Universitat Politècnica de València = Universitad Politecnica de Valencia = Polytechnic University of Valencia

Typical strategies for reducing the computational cost of contact mechanics models use low-rank approximations. The underlying hypothesis is the existence of a low-dimensional subspace for the displacement field and a { non-negative low-dimensional subcone for the contact pressure}. However, given the local nature of contact, it seems natural to wonder whether low-rank approximations are a good fit for contact mechanics or not. In this paper, we investigate some of their limitations and provide numerical evidence showing that contact pressure is linearly inseparable in many practical cases. To this end, we consider various mechanical problems involving non-adhesive frictionless contacts and analyse the performance of the low-rank models in terms of three different criteria, namely compactness, generalization and specificity.

Mots clés: Contact mechanics; Variational inequalites; Model order reduction; Reduced order model; Low-rank approximation

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Génie mécanique [physics.class-ph]; Mécanique des structures [physics.class-ph]

Kiran Sagar Kollepara, José M Navarro‐jiménez, Yves Le Guennec, Luisa Silva, José V Aguado. On the limitations of low‐rank approximations in contact mechanics problems. International Journal for Numerical Methods in Engineering, 2023, 124 (1), pp.217-234. ⟨10.1002/nme.7118⟩. ⟨hal-03918970⟩